SU(2) theory with 4 ﬂavors and Gaiotto’s duality

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9 $S U (2)$ theory with 4 ﬂavors and Gaiotto’s duality

In this section we start with the analysis of $S U (2)$ gauge theory with $N_{f} = 4$ ﬂavors. We will see that it can naturally generalized to the analysis of a whole zoo of theories with the gauge group of the form $S U {(2)}^{n}$ . The discussions basically follow the ﬁrst half of the seminal paper [8].

9.1 The curve as

λ^{2} = ϕ_{2} (z)

9.2 Identiﬁcation of parameters
  9.2.1 Coupling constant
  9.2.2 Mass parameters
9.3 Weak-coupling limit and trifundamentals
9.4 Strong-coupling limit
9.5 Generalization
  9.5.1 Trivalent diagrams
  9.5.2 Example: torus with one puncture
  9.5.3 Example: sphere with ﬁve punctures
  9.5.4 Example: a genus-two surface
  9.5.5 The curve and the Hitchin ﬁeld
9.6 Theories with less ﬂavors revisited
  9.6.1 Rewriting of the curves
  9.6.2 Generalization

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